In general, disposable absorbent inserts may be engaged with reusable outer covers to form wearable absorbent articles, such as a taped diaper, a pant, or an adult incontinence product. The outer covers may comprise one or more insert fastener components configured to be engaged with one or more fastener components on disposable absorbent inserts. While various fastener component configurations between an insert and an outer cover are generally known, improved fastener component configurations should be developed. Especially important are fastener component configurations that allow for attachment of the disposable absorbent insert to the reusable outer cover when the reusable outer cover is in the form of a closed waist pant or a closed waist adult incontinence product.